Crazy violent people are still relatively rare. In the financial district (where I work), things have been relatively calm. A lack of workers also means no panhandlers, but there are more workers lately.
The police also do work somewhat in the nicer neighborhoods.
One thing I've noticed is that black people are much quicker to violence nowadays. The slightest perceived insult, they're ready to go straight to blows. It's a crowded subway, the train hits a bump and you bump into someone, then all of a sudden they're looking to fight.